{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "btw4g5",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Problem 1 Instructions\n",
    "----\n",
    "Compute the requested confidence interval for the population mean given the data below. Do not use the function you create in problem set 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "t4wq5q",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### 1.1 \n",
    "Compute a 95% double-sided confidence interval (2.5% to 97.5%)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "bth4as5ga4gf",
     "locked": false,
     "points": 2,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.41 +/- 1.74\n"
     ]
    }
   ],
   "source": [
    "data = [-4.4,-10.1,1.6,4.0,3.4,-2.0,-5.8,-1.9,-3.1,1.8,-2.9,4.9,2.7,-9.5,2.8,4.3,-1.1,3.9,-9.1,5.6,1.1,-1.0,0.7,9.7,-1.6,-2.3,1.4,2.5,-9.0,1.1]\n",
    "\n",
    "### BEGIN SOLUTION\n",
    "import scipy.stats as stats\n",
    "x = np.mean(data)\n",
    "s = np.std(data, ddof=1)\n",
    "Z = stats.norm.ppf(0.975)\n",
    "print('{:.2f} +/- {:.2f}'.format(x, s * Z / np.sqrt(len(data))))\n",
    "### END SOLUTION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "btrg5r4qgq5",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### 1.2\n",
    "Compute an 80% double-sided confidence interval using the data above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "bvtrabtn",
     "locked": false,
     "points": 2,
     "schema_version": 1,
     "solution": true
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.41 +/- 1.14\n"
     ]
    }
   ],
   "source": [
    "Z = stats.norm.ppf(0.90)\n",
    "print('{:.2f} +/- {:.2f}'.format(x, s * Z / np.sqrt(len(data))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "btranbtyabtrwath",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### 1.3\n",
    "Compute a 95% double-sided confidence interval using the data below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "bgtrata",
     "locked": false,
     "points": 2,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.88 +/- 3.57\n"
     ]
    }
   ],
   "source": [
    "data = [11.5,10.1,20.5,12.4,7.9,9.1,18.1,13.4]\n",
    "\n",
    "### BEGIN SOLUTION\n",
    "x = np.mean(data)\n",
    "s = np.std(data, ddof=1)\n",
    "T = stats.t.ppf(0.975, df=len(data))\n",
    "print('{:.2f} +/- {:.2f}'.format(x, s * T / np.sqrt(len(data))))\n",
    "### END SOLUTION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "btaeratt",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### 1.4\n",
    "Using the same data above, compute a 95% double-sided confidence assuming the population standard deviation is 5.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "btafraf",
     "locked": false,
     "points": 2,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.88 +/- 3.46\n"
     ]
    }
   ],
   "source": [
    "Z = stats.norm.ppf(0.975)\n",
    "print('{:.2f} +/- {:.2f}'.format(x, 5 * Z / np.sqrt(len(data))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "ntrwtrw",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Problem 2 Instructions\n",
    "-----\n",
    "\n",
    "Plot the following quantities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "bteragrae",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### 2.1\n",
    "Plot a standard normal distribution. Typically, plotting from $\\mu-5\\sigma$ to $\\mu + 5\\sigma$ is a good choice when plotting normal distributions. Label your axes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "trsrfge",
     "locked": false,
     "points": 4,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
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DYdcTNDMba2Yvm9l2M9tqZl8Ku6aeYmapZvaOmf057FqCoLBIEGY2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\nEZG4FBYiIhKXwkJEROL6v+qqQTGUeDjBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fec20750438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#make some ponits\n",
    "x = np.linspace(-5, 5, 500)\n",
    "#plot them using the scipystats norm pdf\n",
    "plt.plot(x, stats.norm.pdf(x))\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('P(x)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "getrarefa",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### 2.2\n",
    "Plot the uncertainty in the population mean, $\\mu - \\bar{x}$ vs $P(\\mu - \\bar{x})$, given that we know the population standard deviation is 0.25 and we have 7 samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "bterarfare",
     "locked": false,
     "points": 8,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fec3ca5f828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#get standard error from this info\n",
    "se = 0.25 / np.sqrt(7)\n",
    "#make 500 points from -5 sigma to 5 sigma \n",
    "x = np.linspace(-5 * se, 5 * se, 500)\n",
    "plt.plot(x, stats.norm.pdf(x, scale=se))\n",
    "plt.xlabel('$x - \\mu$')\n",
    "#prefix with r to allow curly braces\n",
    "plt.ylabel(r'$P(\\bar{x} - \\mu)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "btasrfreasf",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### 2.3\n",
    "Plot the probability of the population mean with a sample mean of 3.5 and sample standard deviation of 1.2. Plot it for 3, 5, 10, and 25 samples. Be sure to create a legend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "bnaetrgfretas",
     "locked": false,
     "points": 10,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OAogQHlS/fqMzebDq1QcfmcrrWa096jlReeK/hwQQITzoSBqTrk3jBddsLuEZgYGBWK1W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\njyrXDocAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fec3ca65908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#make points consistent for all graphs\n",
    "#use widest possible one\n",
    "x = np.linspace(-5 * 1.2 / np.sqrt(3) + 3.5, 5 * 1.2 / np.sqrt(3) + 3.5, 1000)\n",
    "#iterate over sample count and plot\n",
    "for N in [3, 5, 10, 25]:\n",
    "    se = 1.2 / np.sqrt(N)    \n",
    "    plt.plot(x, stats.t.pdf(x, loc=3.5, scale=se,df=N), label='N = {}'.format(N))\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('$\\mu$')\n",
    "plt.ylabel(r'$P(\\mu)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "2344g4",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### 2.4\n",
    "Plot the probability of the population mean with a sample mean of 5, a sample standard deviation of 3.2, and 8 samples. Using the `fill_between` command, also color the area corresponding to a 95% double-sided confidence interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false,
    "nbgrader": {
     "grade": true,
     "grade_id": "hb4qw5",
     "locked": false,
     "points": 8,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CQ9LCrzbVc0kkzCJNvz5s3HhpAWc6nf9Yvy/oUiQACg8Z9k6e7eQP249w/bR8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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fec1b219240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#get standard error from this info\n",
    "se = 3.2 / np.sqrt(8)\n",
    "\n",
    "#make 500 points from -5 sigma to 5 sigma \n",
    "x = np.linspace(-5 * se + 5, 5 * se + 5, 500)\n",
    "plt.plot(x, stats.norm.pdf(x, scale=se, loc=5))\n",
    "y = stats.t.ppf(0.975, df=8)\n",
    "x2 = np.linspace(5 - y * se, 5 + y * se, 500)\n",
    "plt.fill_between(x2,stats.norm.pdf(x2, scale=se, loc=5), color='lightgray')\n",
    "plt.xlabel('$\\mu$')\n",
    "#prefix with r to allow curly braces\n",
    "plt.ylabel(r'$P(\\mu)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "nbtrstr",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Problem 3 Instructions\n",
    "----\n",
    "\n",
    "State what distribution the following data follows and compute or plot the requested property."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "ntyrss",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### 3.1\n",
    "\n",
    "The proportion of students graduating at colleges follows a Beta distribution. Each year, a college rankings agency compiles these rates for 100 colleges and also reports the average. If the sample mean and sample standard deviation are 0.74 and 0.21, respectively, what is the population mean for all colleges with 95% confidence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "btrqegrqegr",
     "locked": false,
     "points": 3,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.74 +/- 0.04\n"
     ]
    }
   ],
   "source": [
    "Z = stats.norm.ppf(0.975)\n",
    "print('{} +/- {:.2f}'.format(0.74, 0.21 * Z / np.sqrt(100)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "45thtrye",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### 3.2\n",
    "The number of fatalities due to work related injuries follows a Poisson distribution at each job site. OSHA computes the average for each state taken from 45 random job sites. All numbers are in fatalities per thousand workers. Alaska has a sample mean of 7.4 a sample standard deviation of 6.0 and Texas has a sample mean of 5.3 with a sample standard deviation of 2.3. Plot the probability for the population mean number of accidents per thousand workers for these two states."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "asebtrsgtr",
     "locked": false,
     "points": 8,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HR/flhc83snzLHr/DMW2UJQXTPLu/c+r0/axbT3On1vKwsXnRpp3MWJTLNeP7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\ns9Kc6dBNi/meFEQkGlgLnAb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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fec207e1588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#get standard error from this info\n",
    "se1 = 6.0 / np.sqrt(45)\n",
    "se2 = 2.3 / np.sqrt(45)\n",
    "#some trial and error to get this number\n",
    "x = np.linspace(2, 12, 1000)\n",
    "plt.plot(x, stats.norm.pdf(x, scale=se1, loc=7.4), label='Alaska')\n",
    "plt.plot(x, stats.norm.pdf(x, scale=se2, loc=5.3), label='Texas')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('Fatalities per Thousand Workers')\n",
    "#prefix with r to allow curly braces\n",
    "plt.ylabel('Probability')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Create Assignment",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}